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By Matti Pitkänen


Abstract. Riemann hypothesis is proven by reducing the vanishing of Riemann Zeta to an orthogonality condition for the eigenfunctions of a non-Hermitian operator having the zeros of Riemann Zeta as its eigenvalues. Eigenfunctions are analogous to the so called coherent states and in general not orthogonal to each other. The construction of the operator is inspired by the conviction that Riemann Zeta is associated with a physical system allowing superconformal transformations as its symmetries. The proof as such is elementary involving only basic facts about the theory of Hilbert space operators and complex analysis. 1

Year: 2001
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